The objective of this work is the characterization of the Wyner-Ziv rate-distortion function for memoryless continuous sources, when the correlation between the sources is modeled via an additive noise channel. Modeling the distribution of the correlation noise via a Gaussian mixture, with discrete or continuous mixing variable, provides a unified signal model able to describe a wide class of distributions, useful in the context of practical applications. The Wyner-Ziv rate-distortion function associated with this signal model cannot, in general, be obtained in analytical form. This work contributes a method for its analysis, by providing computable upper and lower bounds.